Lecture 1. Very basic
properties of free groups
Lectures 2-3. Nielsen-Schreier Theorem (subgroups of
free groups are free).
Lectures 4-5. Presentations of groups by generators
and relations. Finitely and infinitely presented groups.
Lecture 6. Residually
Lectures 7-8. Automorphism groups of free groups.
Lecture 9. Free
Lecure 10. Amalgams
(briefly) and HNN-extensions.
Lecture 11. Word growth in groups.
Examples and overview.
Lectures 12-13. Nilpotent groups have polynomial growth (Wolf's
Lecture 14. Growth in
solvable groups (Milnor-Wolf theorem)
Lecture 15. Free Lie
Lectures 16-17. Lie and associative rings corresponding to groups
Lecture 18. Burnside
problems. Puchta's construction.
Lectures 19-20. Golod-Shafarevich inequality and
Lecture 21. Linear
groups. Burnside problem for linear groups.
General Burnside problem for linear groups. Kolchin theorem.
Zariski topology. Lie-Kolchin theorem.
Upcoming lecures (plan):
Malt'sev theorem (finitely generated linear groups are